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Hanoi revisited

Published online by Cambridge University Press:  17 October 2016

Tamsin Forbes  and
Tony Forbes
Tamsin Forbes
Affiliation:
22 St Albans Road, Kingston upon Thames KT2 5HQ
Tony Forbes
Affiliation:
Dept. of Mathematics & Statistics, The Open University MK7 6AA
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Extract

We consider a simple extension of the familiar Tower of Hanoi puzzle. There are three vertical pegs lined up in a row and n discs. The discs have holes in their centres so that they can be threaded on to the pegs. Initially, all n discs are placed on the left-hand peg in non-increasing order of radius to form a tower, as in Figure 1. The object of the game is to transfer the entire tower to the right-hand peg by moving discs from peg to peg, one at a time according to the rules:

  • (1) only a disc at the top of a tower may be moved;

  • (2) a disc must never be placed on top of a smaller disc.

Type
Articles
Information
The Mathematical Gazette , Volume 100 , Issue 549 , November 2016 , pp. 435 - 441
Copyright
Copyright © Mathematical Association 2016 

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References

1. Lucas, É., Récréations Mathématiques, Vol. III, Gauthier-Villars (1893).Google Scholar
2. Berlekamp, E. R., Conway, J. H. and Guy, R. K., Winning ways for your mathematical plays, Vol. 2: Games in particular, Academic Press (1982).Google Scholar
3. Sloane, N. J. A., The On-line Encyclopedia of Integer Sequences, accessed June 2016 at https://oeis.org/ Google Scholar
4. Lind, D. A., On a class of nonlinear binomial sums, Fibonacci Quarterly 3 (1965) pp. 292–298.Google Scholar